CAIE IGCSE Mathematics Extended Number Question Bank

Practise CAIE IGCSE Number through integers, fractions, percentages, ratio, bounds, time, money, indices and standard-form calculations.

Covered syllabus points

E1.1 Types of number E1.2 Sets E1.3 Powers and roots E1.4 Fractions, decimals and percentages E1.5 Ordering E1.6 The four operations E1.7 Indices I E1.8 Standard form E1.9 Estimation E1.10 Limits of accuracy E1.11 Ratio and proportion E1.12 Rates E1.13 Percentages E1.14 Using a calculator E1.15 Time E1.16 Money E1.17 Exponential growth and decay E1.18 Surds

[Maximum number: 6]

(a)

Find the lowest common multiple (LCM) of 30 and 75.

[ 2 ]

150
B1 for answer $150k$
or M1 for prime factors of 30 or 75 seen, a list of multiples of both 30 and 75 with at least 3 of each, $\frac{30\times75}{15}$ oe, or answer $2\times3\times5^2$

(b)

Share $\$608$ in the ratio 4:5:7.
$ $\qquad$ $ $\qquad$ $

[ 3 ]

152
190
266
Accept in any order
B2 for two correct answers
or M1 for $\frac{608}{4+5+7}\times k$ oe where k=1,4,5,7

(c)

Write $0.\dot{2}\dot{7}$ as a fraction.

[ 1 ]

$\frac{27}{99}$ oe fraction

[Maximum number: 5]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

Use set notation to describe the shaded region in the Venn diagram.

[ 1 ]

$A\cap B$

(b)

Shade the correct region in each Venn diagram.

Figure for Question (b) — CAIE IGCSE Mathematics Extended

[ 2 ]

(c)

Figure for Question (c) — CAIE IGCSE Mathematics Extended

50 students are asked if they like English ( E ) and if they like mathematics ( M ). 3 say they do not like English and do not like mathematics.
33 say they like English.
42 say they like mathematics.

[ 2 ]

(i)

Complete the Venn diagram.

[ 2 ]

[Maximum number: 1]

Calculate $\sqrt[4]{39\frac{1}{16}}$ .

[Maximum number: 2]

(a)

The exchange rate is 1 euro =$ 1.142.

(i)

Johann changes $ 500 into euros.

Calculate the number of euros Johann receives.
Give your answer correct to the nearest euro.

438 cao

2

M1 for $\frac{500}{1.142}$

(b)

Lucy spends $\frac{3}{8}$ of the money she has saved this month on a book that costs $\$ 5.25$ .

Calculate how much money Lucy has saved this month.
$

[ 2 ]

14

2

M1 for $5.25 \times \frac{8}{3}$ oe

(c)

Kamal invests $ 6130 at a rate of r % per year compound interest.

The value of his investment at the end of 5 years is $ 6669.
Calculate the value of r.
r=

1.7[0] or 1.699...

M2 for $\sqrt[5]{\frac{6669}{6130}}$
or M1 for $6669=6130k^5$

[Maximum number: 2]

Find the value of $64^{\frac23}$ .

[Maximum number: 9]

(a)

At a football club, season tickets are sold for seated areas and for standing areas.
The cost of season tickets are in the ratio seated : standing = 5 : 3.
The cost of a season ticket for the standing area is $45.
Find the cost of a season ticket for the seated area.

[ 2 ]

75
M1 for $\frac{45}{3}\times k$ , where k is 1, 5 or 8

(b)

In 2021, the value of the team's players was $2.65 million.
In 2022 this value has decreased by 12%.
Find the value in 2022.
$ million

[ 2 ]

2.332 oe
M1 for $2.65\left(1-\frac{12}{100}\right)$ oe
or B1 for 0.318 [million] seen

(c)

The number of people at a football match is 1455.

This is 6.25% of the total number of people allowed in the stadium.
Find the total number of people allowed in the stadium.

[ 2 ]

23280 cao
M1 for $\frac{6.25}{100}\times x=1455$ or better

(d)

The average attendance increased exponentially by 4% each year for the three years from 2016 to 2019.
In 2019 the average attendance was 1631.
Find the average attendance for 2016.

[ 3 ]

1450 or 1449 to 1450
M2 for $1631=k\left(1+\frac4{100}\right)^3$ oe
or B1 for $\left(1+\frac4{100}\right)^3$ oe seen
or M1 for $1631=k\left(1+\frac4{100}\right)^n, n>0$ oe

All question bank results loaded

Covered syllabus points

1. Number question 1

Question (a)

Question (b)

Question (c)

1. Number question 2

Question (a)

Question (b)

Question (c)

Question (i)

1. Number question 3

1. Number question 4

Question (a)

Question (i)

Question (b)

Question (c)

1. Number question 5

1. Number question 6

Question (a)

Question (b)

Question (c)

Question (d)